Question: The following line passes through point $(4, 7)$ : $y = \dfrac{5}{3} x + b$ What is the value of the $y$ -intercept $b$ ?
Substituting $(4, 7)$ into the equation gives: $7 = \dfrac{5}{3} \cdot 4 + b$ $7 = \dfrac{20}{3} + b$ $b = 7 - \dfrac{20}{3}$ $b = \dfrac{1}{3}$ Plugging in $\dfrac{1}{3}$ for $b$, we get $y = \dfrac{5}{3} x + \dfrac{1}{3}$. ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ $(4, 7)$